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Find the magnitude of the magnetic field...

Find the magnitude of the magnetic field at the origin O due to very long conductor carrying current I of the shape as shown in figure.

Text Solution

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Total magnetic field at O is
`vecB_0=vecB_1+vecB_3=(mu_0)/(4pi)I/r(-hati)+(mu_0)/(4pi)I/r(pi/2)(-hatk)+0 ( :'B_3=0)`
`=-(mu_0)/(4pi)I/r[hati+(pihatk)/(2)]=-(mu_0I)/(4r)[hati/pi+hatk/2]`
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